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📐 Mathematics  ·  Vector Algebra  ·  JEE

The vectors |a| = 3, |b| = 2, a.b = 4. The angle theta satisfies:

Answer: cos(theta) = 2/3.

  • A cos(theta) = 2/3
  • B cos(theta) = 1
  • C cos(theta) = 2
  • D cos(theta) = 4/3

Correct answer: A. cos(theta) = 2/3

Explanation: cos(theta) = a.b / (|a||b|) = 4/(3 x 2) = 4/6 = 2/3. theta = cos<sup>-1</sup>(2/3).

xya (4,1)b (2,3)a + b (6,4)

Triangle law of vector addition: placing vector b at the head of vector a, the diagonal from the start to the final head gives the resultant a + b.

Concept context

Vectors, dot product, cross product, and geometric applications

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